Description Usage Arguments Details Value Author(s) References See Also Examples

Compute the prediction loss of a model.

1 2 3 4 5 6 7 8 9 |

`y` |
a numeric vector or matrix giving the observed values. |

`yHat` |
a numeric vector or matrix of the same dimensions as |

`includeSE` |
a logical indicating whether standard errors should be computed as well. |

`trim` |
a numeric value giving the trimming proportion (the default is 0.25). |

`mspe`

and `rmspe`

compute the mean squared prediction error and
the root mean squared prediction error, respectively. In addition,
`mape`

returns the mean absolute prediction error, which is somewhat
more robust.

Robust prediction loss based on trimming is implemented in `tmspe`

and
`rtmspe`

. To be more precise, `tmspe`

computes the trimmed mean
squared prediction error and `rtmspe`

computes the root trimmed mean
squared prediction error. A proportion of the largest squared differences
of the observed and fitted values are thereby trimmed.

Standard errors can be requested via the `includeSE`

argument. Note that
standard errors for `tmspe`

are based on a winsorized standard
deviation. Furthermore, standard errors for `rmspe`

and `rtmspe`

are computed from the respective standard errors of `mspe`

and
`tmspe`

via the delta method.

If standard errors are not requested, a numeric value giving the prediction loss is returned.

Otherwise a list is returned, with the first component containing the prediction loss and the second component the corresponding standard error.

Andreas Alfons

Tukey, J.W. and McLaughlin, D.H. (1963) Less vulnerable confidence and
significance procedures for location based on a single sample:
Trimming/winsorization. *Sankhya: The Indian Journal of Statistics,
Series A*, **25**(3), 331–352

Oehlert, G.W. (1992) A note on the delta method. *The American
Statistician*, **46**(1), 27–29.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
# fit an MM-regression model
library("robustbase")
data("coleman")
fit <- lmrob(Y~., data=coleman)
# compute the prediction loss from the fitted values
# (hence the prediction loss is underestimated in this simple
# example since all observations are used to fit the model)
mspe(coleman$Y, predict(fit))
rmspe(coleman$Y, predict(fit))
mape(coleman$Y, predict(fit))
tmspe(coleman$Y, predict(fit), trim = 0.1)
rtmspe(coleman$Y, predict(fit), trim = 0.1)
# include standard error
mspe(coleman$Y, predict(fit), includeSE = TRUE)
rmspe(coleman$Y, predict(fit), includeSE = TRUE)
mape(coleman$Y, predict(fit), includeSE = TRUE)
tmspe(coleman$Y, predict(fit), trim = 0.1, includeSE = TRUE)
rtmspe(coleman$Y, predict(fit), trim = 0.1, includeSE = TRUE)
``` |

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